How can I reset all custom properties into a "Redo Panel"?
Ditch your operator and use the one designed for this.
As a suggestion, add imports and register etc to question code, to make a minimal run-able example.  This would only be a couple of lines and is appreciated by those answering not to have to do this themselves. (It adds up)
There is no need to re-invent the wheel and write a new nested operator to reset the defaults of another. Simply use the one designed to do this.

bpy.ops.wm.operator_defaults()
Set the active operator to its default values

eg in the layout of the operator to restore defaults.
layout.operator(&quot;wm.operator_defaults&quot;)

Would strongly consider looking at the 'PRESETS' system for operators, or using addon preferences to set and save preferences.  Reset to defaults and settings prior are lost. Blender will start with the defaults.
As mentioned in comments the reset single or all to defaults is available via context menu (right click over property).
To have an operator always invoke with defaults see Force a Blender operator to always start with default values